In this work we prove that the shallow water flow, subject to strong wind
forcing and linearized around an adequate stationary profile, develops for
large times closed trajectories due to the propagation of Rossby waves, while
Poincar\'e waves are shown to disperse. The methods used in this paper involve
semi-classical analysis and dynamical systems for the study of Rossby waves,
while some refined spectral analysis is required for the study of Poincar\'e
waves, due to the large time scale involved which is of diffractive type
